66
<Example 6>
The hot water inside an electric pot is maintained at 92 C.
When a thermometer is placed in this hot water, the values indicated by the
thermometer at times x and the differences y between these values and the
temperature of the hot water are shown below. Using Euler's exponential
regression, find the formula that expresses the relation between each time x
and the temperature difference y.
Operation
0 67
4
40
...
37
1
Temperature difference y [ C] from liquid
(Room temperature 25 C, hot water temperature 92 C)
Time x [S]
Thermometer temperature [ C]
0
4
8
12
16
20
24
28
32
36
40
25
55
71
79
85
88
90
90
91
91
91
67
37
21
13
7
4
2
2
1
1
1
e: Napier's constant
e=2.718281828
…
Display
When x and y are in the following relationship, use Euler's exponential regression to find the
coefficients a and b of the relational expression y = ae
bx
, and the correlation coefficient r.
0
x y
4
8
12
16
20
24
28
32
36
40
67
37
21
13
7
4
2
2
1
1
1
Correlation coefficient
r 1
Correlation exists
Fig. 1 Fig. 2 Fig. 3
Correlation exists No correlation
r -1 r = 0
y
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x x
y y
DATA
DATA
(Close the input table.)
S TAT
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